IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i13p2196-d1695293.html
   My bibliography  Save this article

Extremum Seeking for the First Derivative of Nonlinear Maps with Constant Delays via a Time-Delay Approach

Author

Listed:
  • Jianzhong Li

    (School of Information and Control Engineering, Southwest University of Science and Technology, Mianyang 621010, China
    College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China)

  • Hongye Su

    (College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China)

  • Yang Zhu

    (College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, China)

Abstract

This paper introduces an extremum seeking (ES) scheme for the unknown map’s first derivative by tailoring a demodulation signal in which the closed-loop system is subject to constant transmission delays. Unlike most publications that manage delays using predictor-based methods, we are concerned with the delay-robustness of the introduced ES system via the newly developed time-delay approach. The original ES system is transformed to a nonlinear retarded-type plant with disturbances and the stability condition in the form of linear matrix inequalities is achieved. When the related bounds of the nonlinear map are not known, a rigorous practical stability proof is provided. Second, and more importantly, under the availability of prior knowledge about the nonlinear map, we are able to provide a quantitative calculation on the maximum allowable delay, the upper bound of the dither period, and the ultimate seeking error. Numerical examples are offered to exemplify the effectiveness of the proposed method.

Suggested Citation

  • Jianzhong Li & Hongye Su & Yang Zhu, 2025. "Extremum Seeking for the First Derivative of Nonlinear Maps with Constant Delays via a Time-Delay Approach," Mathematics, MDPI, vol. 13(13), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2196-:d:1695293
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/13/2196/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/13/2196/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cesar Ulises Solís-Cervantes & Sergio Isai Palomino-Resendiz & Diego Alonso Flores-Hernández & Marco Antonio Peñaloza-López & Carlos Manuel Montelongo-Vazquez, 2024. "Design and Implementation of Extremum-Seeking Control Based on MPPT for Dual-Axis Solar Tracker," Mathematics, MDPI, vol. 12(12), pages 1-22, June.
    2. Yang Tian & Ning Pan & Maobo Hu & Haoping Wang & Ivan Simeonov & Lyudmila Kabaivanova & Nicolai Christov, 2023. "Newton-Based Extremum Seeking for Dynamic Systems Using Kalman Filtering: Application to Anaerobic Digestion Process Control," Mathematics, MDPI, vol. 11(1), pages 1-15, January.
    3. Hoai Vu Anh Truong & Hoai An Trinh & Tri Cuong Do & Manh Hung Nguyen & Van Du Phan & Kyoung Kwan Ahn, 2024. "An Enhanced Extremum Seeking-Based Energy Management Strategy with Equivalent State for Hybridized-Electric Tramway-Powered by Fuel Cell–Battery–Supercapacitors," Mathematics, MDPI, vol. 12(12), pages 1-22, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haobin Jiang & Yang Zhao & Shidian Ma, 2025. "Dual-Layer Energy Management Strategy for a Hybrid Energy Storage System to Enhance PHEV Performance," Energies, MDPI, vol. 18(7), pages 1-20, March.
    2. Abdul-Hussein, Mustafa A. & Mohammed, Jamal A.-K. & Abdul-Lateef, Wisam E., 2025. "Design and implementation of pneumatic actuators in a dual-axis solar tracker under the climatic conditions of karbala city," Renewable Energy, Elsevier, vol. 239(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2196-:d:1695293. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.